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Liveness in Rewriting # Jurgen Giesl 1 and Hans Zantema 2

Summary: Liveness in Rewriting #
J˜urgen Giesl 1 and Hans Zantema 2
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany,
2 Department of Computer Science, TU Eindhoven, P.O. Box 513,
5600 MB Eindhoven, The Netherlands, h.zantema@tue.nl
Abstract. In this paper, we show how the problem of verifying liveness
properties is related to termination of term rewrite systems (TRSs). We
formalize liveness in the framework of rewriting and present a sound and
complete transformation to transform particular liveness problems into
TRSs. Then the transformed TRS terminates if and only if the original
liveness property holds. This shows that liveness and termination are
essentially equivalent. To apply our approach in practice, we introduce a
simpler sound transformation which only satisfies the `only if'­part. By
refining existing techniques for proving termination of TRSs we show how
liveness properties can be verified automatically. As examples, we prove
a liveness property of a waiting line protocol for a network of processes
and a liveness property of a protocol on a ring of processes.
1 Introduction
Usually, liveness is roughly defined as: ``something will eventually happen'' [1] and


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences